E the least squares estimate based on the data x1 y 1

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Unformatted text preview: of parameters we wish to estimate, and P ∈ Rm×m is a permutation matrix. (This means that each row and column of P has exactly one entry equal to one, and the remaining m − 1 entries zero.) We assume that m > n and that at most k of the measurements are permuted; i.e., P ei = ei for no more than k indices i. We are interested in the case when k < m (e .g . k = 0.4m); that is, only some of the measurements have been permuted. We want to estimate x and P . ˆ Once we make a guess P for P , we can get the maximum likelihood estimate of x by minimizing ˆ T y 2 . The residual Ax − P T y is then our guess of what P T v is, and should be consistent Ax − P ˆˆ with being a sample of a N (0, I ) vector. In principle, we can find the maximum likelihood estimate of x and P by solving a set of m (k ! − 1) k least-squares problems, and choosing one that has minimum residual. But this is not practical unless m and k are both very small. Describe a heuristic method for approximately so...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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